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Application of the maximum algorithm to the lipkin model

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Abstract

Lipkin constructed a many-Fermion system which, despite the simplicity of its Hamiltonian, exhibits features of complex systems. Application of the maximum algorithm is attempted in order to find the ground-state level. Numerical computations suggest that eigenstates of a particular parity transformation introduced by Lipkin have many advantages. Coupling of two models provides a means of studying the maximum method in the product space generated by the two subsystems.

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References

  1. Lipkin, H. J., Meshkov, N., Glick, A. J., (1965).Nuclear Physics,62, 188.

  2. Lipkin, H. J., (1966).Lie Groups for Pedestrians, Chap 2. North-Holland, Amsterdam.

  3. Textor, W. (1978).International Journal of Theoretical Physics,8, 599.

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Textor, W. Application of the maximum algorithm to the lipkin model. Int J Theor Phys 19, 485–495 (1980). https://doi.org/10.1007/BF00671815

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Keywords

  • Field Theory
  • Complex System
  • Elementary Particle
  • Numerical Computation
  • Quantum Field Theory